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- W4287557178 abstract "A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:{0,1}^n to {0,1}^n$. This model finds applications in biology, where fixed points play a central role. For example, in genetic regulations, they correspond to cell phenotypes. In this context, experiments reveal the existence of positive or negative influences among components: component $i$ has a positive (resp. negative) influence on component $j$ meaning that $j$ tends to mimic (resp. negate) $i$. The digraph of influences is called signed interaction digraph (SID), and one SID may correspond to a large number of BNs (which is, in average, doubly exponential according to $n$). The present work opens a new perspective on the well-established study of fixed points in BNs. When biologists discover the SID of a BN they do not know, they may ask: given that SID, can it correspond to a BN having at least/at most $k$ fixed points? Depending on the input, we prove that these problems are in $textrm{P}$ or complete for $textrm{NP}$, $textrm{NP}^{textrm{NP}}$, $textrm{NP}^{textrm{#P}}$ or $textrm{NEXPTIME}$. In particular, we prove that it is $textrm{NP}$-complete (resp. $textrm{NEXPTIME}$-complete) to decide if a given SID can correspond to a BN having at least two fixed points (resp. no fixed point)." @default.
- W4287557178 created "2022-07-25" @default.
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- W4287557178 date "2021-11-23" @default.
- W4287557178 modified "2023-10-08" @default.
- W4287557178 title "Complexity of fixed point counting problems in Boolean Networks" @default.
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